Due to the centralized importance of spectroscopic methods in experimental physical chemistry, a primary directive in the field of quantum chemistry is to be able to accurately and efficiently predict and interpret the response behavior of molecular systems in the presence of external perturbations. In electronic structure theory, molecular response properties may be described, in general, as a large system of linear equations involving the inverse of the quantum propagator that must be solved iteratively. If the spectral region of interest is deep<br/>in the interior of, or dense in the propagator's eigenspectrum or if the desired spectral resolution is very high, traditional methods such as eigendecomposition and solving the response problem directly become computationally intractable. In this work, we present a novel, automatic model order reduction (MOR) algorithm with moment matching for the evaluation of general molecular response properties. In essence, the purposed algorithm maps the full molecular response problem onto an equivalent problem of reduced dimension via a careful selection of interpolation points. As the dimension of the reduced problem is often orders of magnitude less than the full problem, the computational complexity for the MOR problem if greatly reduced. Numerical Results are presented for the prediction of X-Ray absorption and X-Ray circular--dichroism spectra using the proposed MOR algorithm with the polarization propagator of time--dependent density functional theory (TD-DFT). Further, the favorable computational cost and scaling of the MOR algorithm is shown in comparison to the<br/>eigenmode TD-DFT and frequency--dependent TD-DFT methods. The proposed MOR algorithm will enable routine, simple inquiry into previously difficult or intractable spectroscoptic problems such as X-Ray absorption and X-Ray circular--dichrosim spectroscopy.

Novel model reduction algorithm for the efficient evaluation of molecular response properties

254th National Meeting (2017)

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